Question

2 mũ x + 2 mũ x+3= 144

2 mũ x-1 + 5.2 mũ x-2= 224

Answer 1

a) \(2^x+2^{x+3}=144\)

\(2^x\left(1+2^3\right)=144\)

\(2^x.9=144\)

\(2^x=144:9=16\)

=> \(2^x=2^4\Rightarrow x=4\)

b) \(2^{x-1}+5.2^{x-2}=224\)

\(2^{x-2}\left(2+5\right)=224\)

\(2^{x-2}.7=224\Rightarrow2^{x-2}=32\Rightarrow2^{x-2}=2^5\)

=> x - 2 = 5 => x = 7

Answer 2

a ) 2^x + 2^{x + 3} = 144
=> 2^x . ( 1 + 2³ ) = 144

=> 2^x . 9  = 144

=> 2^x = 16

=> 2^x = 2⁴

=> x = 4
Vậy x = 4

b ) 2^{x - 1}  + 5. 2^{x - 2} = 224

=> 2^{x - 2} . ( 2 + 5 ) = 224

=> 2^{x - 2} . 7 = 224

=> 2^{x - 2} =  32

=> 2^{x - 2} = 2⁵

=> x - 2 = 5

=> x = 7

Vậy x = 7